Changeset 2293 for research


Ignore:
Timestamp:
Apr 16, 2008, 12:12:05 AM (12 years ago)
Author:
Sam Hocevar
Message:
  • Final version of the paper. Uploaded at the last minute, of course.
Location:
research/2008-displacement
Files:
11 added
1 deleted
13 edited
1 moved

Legend:

Unmodified
Added
Removed
  • research/2008-displacement/README

    r2292 r2293  
    6767set mxtics 2
    6868set mytics 2
     69set xlabel "$dx$"
     70set ylabel "$dy$"
     71unset mztics
     72unset ztics
    6973set size square
    7074set xzeroaxis
    7175set yzeroaxis
    72 set xlabel "dx" font "Italic,32"
    73 splot 'part0/lena-values.txt' with lines
     76set lmargin screen 0.0 #.05
     77set bmargin screen 0.2 # .15
     78set tmargin screen 0.9 #.95
     79set rmargin screen 0.9 #.95
     80set terminal epslatex color size 5,2 blacktext
     81unset colorbox
     82#set lmargin 0.05
     83#set rmargin 0.95
     84#splot 'part0/lena-values.txt' with lines
     85set output "lena-values.tex"
     86splot '../part0/lena-values.txt' with lines lw 3 notitle
     87unset output
     88set term pop
    7489
    7590
     
    128143set xrange [-.1:.4]
    129144set yrange [.4:-.1]
    130 set grid
    131 set lmargin screen 0.05
    132 set bmargin screen 0.15
    133 set tmargin screen 0.95
    134 set rmargin screen 0.95
    135 unset colorbox
    136 set pm3d explicit map interpolate 1.8,1.8
    137 set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
    138 unset key
    139 #splot "histo-fs.txt" notitle
    140 set terminal epslatex color size 1.8,1.8 blacktext
     145set xlabel "$dx$"
     146set ylabel "$dy$"
     147set grid
     148set lmargin screen 0.05
     149set bmargin screen 0.25
     150set tmargin screen 0.95
     151set rmargin screen 0.95
     152unset colorbox
     153set pm3d explicit map interpolate 1.8,1.8
     154set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
     155unset key
     156#splot "../../subblock/histo-fs.txt" notitle
     157set terminal epslatex color size 1.8,2.0 blacktext
    141158set output "fs-histo.tex"
    142 splot "histo-fs.txt" notitle
     159splot "../../subblock/histo-fs.txt" notitle
    143160unset output
    144161set term pop
     
    156173set xrange [-.1:.9]
    157174set yrange [.9:-.1]
    158 set grid
    159 set lmargin screen 0.05
    160 set bmargin screen 0.15
    161 set tmargin screen 0.95
    162 set rmargin screen 0.95
    163 unset colorbox
    164 set pm3d explicit map interpolate 1.8,1.8
    165 set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
    166 unset key
    167 #splot "histo-jajuni.txt" notitle
    168 set terminal epslatex color size 1.8,1.8 blacktext
     175set xlabel "$dx$"
     176set ylabel "$dy$"
     177set grid
     178set lmargin screen 0.05
     179set bmargin screen 0.25
     180set tmargin screen 0.95
     181set rmargin screen 0.95
     182unset colorbox
     183set pm3d explicit map interpolate 1.8,1.8
     184set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
     185unset key
     186#splot "../../subblock/histo-jajuni.txt" notitle
     187set terminal epslatex color size 1.8,2.0 blacktext
    169188set output "jajuni-histo.tex"
    170 splot "histo-jajuni.txt" notitle
     189splot "../../subblock/histo-jajuni.txt" notitle
    171190unset output
    172191set term pop
     
    191210set xrange [-.2:.2]
    192211set yrange [.3:-.1]
    193 set grid
    194 set lmargin screen 0.05
    195 set bmargin screen 0.15
    196 set tmargin screen 0.95
    197 set rmargin screen 0.95
    198 unset colorbox
    199 set pm3d explicit map interpolate 1.8,1.8
    200 set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
    201 unset key
    202 splot "histo-ostro.txt" notitle
    203 set terminal epslatex color size 1.8,1.8 blacktext
     212set xlabel "$dx$"
     213set ylabel "$dy$"
     214set xtics -.2,0.1
     215set grid
     216set lmargin screen 0.05
     217set bmargin screen 0.25
     218set tmargin screen 0.95
     219set rmargin screen 0.95
     220unset colorbox
     221set pm3d explicit map interpolate 1.8,1.8
     222set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
     223unset key
     224splot "../../subblock/histo-ostro.txt" notitle
     225set terminal epslatex color size 1.8,2.0 blacktext
    204226set output "ostro-histo.tex"
    205 splot "histo-ostro.txt" notitle
     227splot "../../subblock/histo-ostro.txt" notitle
    206228unset output
    207229set term pop
     
    220242set xrange [-.5:.2]
    221243set yrange [.6:-.1]
    222 set grid
    223 set lmargin screen 0.05
    224 set bmargin screen 0.15
    225 set tmargin screen 0.95
    226 set rmargin screen 0.95
    227 unset colorbox
    228 set pm3d explicit map interpolate 1.8,1.8
    229 set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
    230 unset key
    231 splot "histo-optimum.txt" notitle
    232 set terminal epslatex color size 1.8,1.8 blacktext
     244set xlabel "$dx$"
     245set ylabel "$dy$"
     246set grid
     247set lmargin screen 0.05
     248set bmargin screen 0.25
     249set tmargin screen 0.95
     250set rmargin screen 0.95
     251unset colorbox
     252set pm3d explicit map interpolate 1.8,1.8
     253set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
     254unset key
     255splot "../../subblock/histo-optimum.txt" notitle
     256set terminal epslatex color size 1.8,2.0 blacktext
    233257set output "optimum-histo.tex"
    234 splot "histo-optimum.txt" notitle
     258splot "../../subblock/histo-optimum.txt" notitle
    235259unset output
    236260set term pop
     
    249273set xrange [-.3:.3]
    250274set yrange [.6:-.1]
    251 set grid
    252 set lmargin screen 0.05
    253 set bmargin screen 0.15
    254 set tmargin screen 0.95
    255 set rmargin screen 0.95
    256 unset colorbox
    257 set pm3d explicit map interpolate 1.8,1.8
    258 set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
    259 unset key
    260 splot "histo-serpopt.txt" notitle
    261 set terminal epslatex color size 1.8,1.8 blacktext
     275set xlabel "$dx$"
     276set ylabel "$dy$"
     277set grid
     278set lmargin screen 0.05
     279set bmargin screen 0.25
     280set tmargin screen 0.95
     281set rmargin screen 0.95
     282unset colorbox
     283set pm3d explicit map interpolate 1.8,1.8
     284set palette model RGB defined(0 "white", 1 "blue", 2 "red", 3 "yellow")
     285unset key
     286splot "../../subblock/histo-serpopt.txt" notitle
     287set terminal epslatex color size 1.8,2.0 blacktext
    262288set output "serpopt-histo.tex"
    263 splot "histo-serpopt.txt" notitle
     289splot "../../subblock/histo-serpopt.txt" notitle
    264290unset output
    265291set term pop
     
    287313cat -n $x | sed 's/^  *[0-9]*\([0-9]\)[[:space:]]*/[\1] /; s/....###/###/; s/\[[27]/[1/; s/\[[38]/[2/; s/\[[49]/[3/; s/\[[50]/[4/'
    288314
    289 #
     315# Convert lena results to cropped detail
     316convert output-7-3-5-1-serp.png -crop 160x160+32+160 crop-7-3-5-1-serp.png
     317convert output-7-4-5-0-serp.png -crop 160x160+32+160 crop-7-4-5-0-serp.png
     318
  • research/2008-displacement/paper/Makefile

    r2277 r2293  
    11all: paper.pdf
    22
    3 paper.pdf: paper.tex fs-histo.tex
     3IMAGES = direction.tex fs-histo.tex jajuni-histo.tex lena-values.tex optimum-histo.tex ostro-histo.tex serpopt-histo.tex
     4
     5paper.pdf: paper.tex $(IMAGES)
    46        latex paper.tex
    57        latex paper.tex
    6         dvipdf paper.dvi
     8        dvips paper.dvi
     9        sed -i 's,/Title.*,/Title (Reinstating Floyd-Steinberg: Improved Metrics for Quality Assessment of Error Diffusion Algorithms),' paper.ps
     10        ps2pdf paper.ps
    711
    812clean:
    9         rm -f paper.log paper.dvi paper.aux paper.pdf
     13        rm -f paper.log paper.dvi paper.aux paper.pdf paper.ps
    1014
  • research/2008-displacement/paper/fs-histo.tex

    r2277 r2293  
    7373  \fi
    7474  \setlength{\unitlength}{0.0500bp}%
    75   \begin{picture}(2590.00,2590.00)%
     75  \begin{picture}(2590.00,2880.00)%
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    420       \csname LTb\endcsname%
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    422       \csname LTb\endcsname%
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    424       \csname LTb\endcsname%
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     404      \csname LTb\endcsname%
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     406      \csname LTb\endcsname%
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     412      \csname LTb\endcsname%
     413      \put(2460,435){\makebox(0,0){\strut{} 0.4}}%
     414      \put(1295,105){\makebox(0,0){\strut{}$dx$}}%
     415      \csname LTb\endcsname%
     416      \put(-42,2735){\makebox(0,0)[r]{\strut{}-0.1}}%
     417      \csname LTb\endcsname%
     418      \put(-42,2332){\makebox(0,0)[r]{\strut{} 0}}%
     419      \csname LTb\endcsname%
     420      \put(-42,1929){\makebox(0,0)[r]{\strut{} 0.1}}%
     421      \csname LTb\endcsname%
     422      \put(-42,1527){\makebox(0,0)[r]{\strut{} 0.2}}%
     423      \csname LTb\endcsname%
     424      \put(-42,1124){\makebox(0,0)[r]{\strut{} 0.3}}%
     425      \csname LTb\endcsname%
     426      \put(-42,721){\makebox(0,0)[r]{\strut{} 0.4}}%
     427      \put(-636,1728){\rotatebox{90}{\makebox(0,0){\strut{}$dy$}}}%
    426428    }%
    427429    \gplbacktext
  • research/2008-displacement/paper/jajuni-histo.tex

    r2277 r2293  
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    7777    }%
     
    362362      \color{black}%
    363363      \csname LTb\endcsname%
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    365       \csname LTb\endcsname%
    366       \put(829,104){\makebox(0,0){\strut{} 0.2}}%
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    370       \put(1761,104){\makebox(0,0){\strut{} 0.6}}%
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    372       \put(2227,104){\makebox(0,0){\strut{} 0.8}}%
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    383385    }%
    384386    \gplbacktext
  • research/2008-displacement/paper/lena-values.tex

    r2292 r2293  
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  • research/2008-displacement/paper/optimum-histo.tex

    r2277 r2293  
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  • research/2008-displacement/paper/ostro-histo.tex

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  • research/2008-displacement/paper/paper.tex

    r2292 r2293  
    102102(LSMB) \cite{lsmb}.
    103103
    104 HVS models are usually low-pass filters. Nasanen \cite{nasanen}, Analoui
    105 and Allebach \cite{allebach} found that using Gaussian models gave visually
    106 pleasing results, an observation confirmed by independent visual perception
    107 studies \cite{mcnamara}.
     104HVS models are usually low-pass filters. Nasanen \cite{nasanen}, Analoui and
     105Allebach found that using Gaussian models gave visually pleasing results, an
     106observation confirmed by independent visual perception studies \cite{mcnamara}.
    108107
    109108DBS yields halftones of impressive quality. However, despite efforts to make
     
    116115Boustrophedonic (serpentine) scanning has been shown to cause fewer visual
    117116artifacts \cite{halftoning}, but other, more complex processing paths such as
    118 Hilbert curves \cite{spacefilling}, \cite{peano} are seldom used as they do not
    119 improve the image quality significantly.
     117Hilbert curves \cite{spacefilling} are seldom used as they do not improve the
     118image quality significantly.
    120119
    121120Intuitively, as the error is always propagated to the bottom-left or
     
    169168Experiments show that for a given image and a given corresponding halftone,
    170169$E_{dx,dy}$ has a local minimum almost always away from $(dx,dy) = (0,0)$ (Fig.
    171 \ref{fig:lena-min}). Let $E$ be an error metric where this remains true. We
     170\ref{fig:lena-values}). Let $E$ be an error metric where this remains true. We
    172171call the local minimum $E_{min}$:
    173172
     
    177176
    178177\begin{figure}
    179   \begin{center}
    180    \input{lena-min}
    181    \caption{Mean square error for the \textit{Lena} image. $v$ is a simple
    182             $11\times11$ Gaussian convolution kernel with $\sigma = 1.2$ and
    183             $(dx,dy)$ vary in $[-1,1]\times[-1,1]$.}
    184    \label{fig:lena-min}
     178  \begin{minipage}[c]{0.8\textwidth}
     179    \input{lena-values}
     180  \end{minipage}
     181  \begin{center}
     182    \caption{Mean square error for the \textit{Lena} image ($\times10^4$). $v$
     183             is a simple $11\times11$ Gaussian convolution kernel with $\sigma
     184             = 1.2$ and $(dx,dy)$ vary in $[-1,1]\times[-1,1]$.}
     185    \label{fig:lena-values}
    185186  \end{center}
    186187\end{figure}
     
    202203we tested two serpentine error diffusion algorithms: Ostromoukhov's simple
    203204error diffusion \cite{ostromoukhov}, which uses a variable coefficient kernel,
    204 and Wong and Allebach's optimum error diffusion kernel \cite{wong}.
     205and Wong and Allebach's optimum error diffusion kernel \cite{wong}:
    205206
    206207\begin{center}
     
    268269the error computed at $(dx,dy)$. As $E_{fast}$ does not depend on the image, it
    269270is a lot faster to compute than $E_{min}$, and as it is statistically closer to
    270 $E_{min}$, we can expect it to be a better error estimation than $E$.
     271$E_{min}$, we can expect it to be a better error estimation than $E$:
    271272
    272273\begin{center}
    273   \begin{tabular}{|l|c|c|c|c|}
    274   \hline
    275   &~ $E\times10^4$ ~&~ $dx$ ~&~ $dy$ ~&~ $E_{fast}\times10^4$ ~\\ \hline
    276   ~raster Floyd-Steinberg ~&~ 3.7902 ~&~ 0.16 ~&~ 0.28 ~&~ 3.3447 ~\\ \hline
    277   ~raster Ja-Ju-Ni        ~&~ 9.7013 ~&~ 0.26 ~&~ 0.76 ~&~ 7.5891 ~\\ \hline
    278   ~Ostromoukhov           ~&~ 4.6892 ~&~ 0.00 ~&~ 0.19 ~&~ 4.6117 ~\\ \hline
    279   ~optimum kernel         ~&~ 7.5209 ~&~ 0.00 ~&~ 0.34 ~&~ 6.8233 ~\\
     274  \begin{tabular}{|l|c|c|c|c|c|}
     275  \hline
     276  &~ $E\times10^4$ ~&~ $E_{min}\times10^4$ ~&~ $dx$ ~&~ $dy$ ~&~ $E_{fast}\times10^4$ ~\\ \hline
     277  ~raster Floyd-Steinberg ~&~ 3.7902 ~&~ 3.1914 ~&~ 0.16 ~&~ 0.28 ~&~ 3.3447 ~\\ \hline
     278  ~raster Ja-Ju-Ni        ~&~ 9.7013 ~&~ 6.6349 ~&~ 0.26 ~&~ 0.76 ~&~ 7.5891 ~\\ \hline
     279  ~Ostromoukhov           ~&~ 4.6892 ~&~ 4.4783 ~&~ 0.00 ~&~ 0.19 ~&~ 4.6117 ~\\ \hline
     280  ~optimum kernel         ~&~ 7.5209 ~&~ 6.5772 ~&~ 0.00 ~&~ 0.34 ~&~ 6.8233 ~\\
    280281  \hline
    281282  \end{tabular}
     
    309310  ~ 1 ~&~ 7 3 6 0 ~&~ 4.65512 ~&~ 3.94217 ~\\ \hline
    310311  ~ 2 ~&~ 8 3 5 0 ~&~ 4.65834 ~&~ 4.03699 ~\\ \hline
    311   ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\ \hline
     312  \hline
    312313  ~ 5 ~&~ 7 3 5 1 ~&~ 4.68588 ~&~ 3.79556 ~\\ \hline
    313   ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\ \hline
     314  \hline
    314315  ~ 18 ~&~ 6 3 5 2 ~&~ 4.91020 ~&~ 3.70465 ~\\ \hline
    315316  ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\
     
    327328  ~ 1 ~&~ 6 3 5 2 ~&~ 3.70465 ~&~ 4.91020 ~\\ \hline
    328329  ~ 2 ~&~ 7 3 5 1 ~&~ 3.79556 ~&~ 4.68588 ~\\ \hline
    329   ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\ \hline
     330  \hline
    330331  ~ 15 ~&~ 7 3 6 0 ~&~ 3.94217 ~&~ 4.65512 ~\\ \hline
    331   ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\ \hline
     332  \hline
    332333  ~ 22 ~&~ 8 3 5 0 ~&~ 4.03699 ~&~ 4.65834 ~\\ \hline
    333334  ~ \dots ~&~ \dots ~&~ \dots ~&~ \dots ~\\
     
    339340coefficients were indeed amongst the best possible for raster scan.
    340341More importantly, using $E$ as the decision variable may have elected
    341 $\frac{1}{16}\{8,4,4,0\}$, which is in fact a poor choice.
     342$\frac{1}{16}\{7,3,6,0\}$ or $\frac{1}{16}\{8,3,5,0\}$, which are in fact poor
     343choices.
    342344
    343345For serpentine scan, however, our experiment suggests that
     
    348350\begin{figure}
    349351  \begin{center}
    350     \includegraphics[width=0.8\textwidth]{lena.eps}
    351     \caption{halftone of \textit{Lena} using serpentine error diffusion and
    352              the optimum coefficients $\frac{1}{16}\{7,4,5,0\}$ that improve
    353              on the standard Floyd-Steinberg coefficients in terms of visual
    354              quality for the HVS model studied in section 3.}
     352    \includegraphics[width=0.4\textwidth]{output-7-3-5-1-serp.eps}
     353    ~
     354    \includegraphics[width=0.4\textwidth]{output-7-4-5-0-serp.eps}
     355  \end{center}
     356  \begin{center}
     357    \includegraphics[width=0.4\textwidth]{crop-7-3-5-1-serp.eps}
     358    ~
     359    \includegraphics[width=0.4\textwidth]{crop-7-4-5-0-serp.eps}
     360    \caption{halftone of \textit{Lena} using serpentine error diffusion
     361             (\textit{left}) and the optimum coefficients
     362             $\frac{1}{16}\{7,4,5,0\}$ (\textit{right}) that improve on the
     363             standard Floyd-Steinberg coefficients in terms of visual quality
     364             for the HVS model used in section 3. The detailed area
     365             (\textit{bottom}) shows fewer structure artifacts in the regions
     366             with low contrast.}
    355367    \label{fig:lena7450}
    356368  \end{center}
     
    419431Computer Graphics (Proceedings of SIGGRAPH 91), 25(4):81--90, 1991
    420432
    421 \bibitem[9]{peano}
    422 I.~H. Witten and R.~M. Neal,
    423 \textit{Using peano curves for bilevel display of continuous-tone images}.
    424 IEEE Computer Graphics \& Appl., 2:47--52, 1982
    425 
    426 \bibitem[10]{nasanen}
     433\bibitem[9]{nasanen}
    427434R. Nasanen,
    428435\textit{Visibility of halftone dot textures}.
    429436IEEE Trans. Syst. Man. Cyb., vol. 14, no. 6, pp. 920--924, 1984
    430437
    431 \bibitem[11]{allebach}
     438\bibitem[10]{allebach}
    432439M. Analoui and J.~P. Allebach,
    433440\textit{Model-based halftoning using direct binary search}.
     
    435442February 1992, San Jose, CA, pp. 96--108
    436443
    437 \bibitem[12]{mcnamara}
     444\bibitem[11]{mcnamara}
    438445Ann McNamara,
    439446\textit{Visual Perception in Realistic Image Synthesis}.
    440447Computer Graphics Forum, vol. 20, no. 4, pp. 211--224, 2001
    441448
    442 \bibitem[13]{bhatt}
     449\bibitem[12]{bhatt}
    443450Bhatt \textit{et al.},
    444451\textit{Direct Binary Search with Adaptive Search and Swap}.
    445452\url{http://www.ima.umn.edu/2004-2005/MM8.1-10.05/activities/Wu-Chai/halftone.pdf}
    446453
    447 \bibitem[14]{4chan}
     454\bibitem[13]{4chan}
    448455moot,
    449456\url{http://www.4chan.org/}
    450457
    451 \bibitem[15]{wong}
     458\bibitem[14]{wong}
    452459P.~W. Wong and J.~P. Allebach,
    453460\textit{Optimum error-diffusion kernel design}.
    454461Proc. SPIE Vol. 3018, p. 236--242, 1997
    455462
    456 \bibitem[16]{ostromoukhov}
     463\bibitem[15]{ostromoukhov}
    457464Victor Ostromoukhov,
    458465\textit{A Simple and Efficient Error-Diffusion Algorithm}.
     
    460467Series, pp. 567--572, 2001
    461468
    462 \bibitem[17]{lsmb}
     469\bibitem[16]{lsmb}
    463470T.~N. Pappas and D.~L. Neuhoff,
    464471\textit{Least-squares model-based halftoning}.
     
    466473CA, Feb. 1992, vol. 1666, pp. 165--176
    467474
    468 \bibitem[18]{stability}
     475\bibitem[17]{stability}
    469476R. Eschbach, Z. Fan, K.~T. Knox and G. Marcu,
    470477\textit{Threshold Modulation and Stability in Error Diffusion}.
    471478in Signal Processing Magazine, IEEE, July 2003, vol. 20, issue 4, pp. 39--50
    472479
    473 \bibitem[19]{sullivan}
     480\bibitem[18]{sullivan}
    474481J. Sullivan, R. Miller and G. Pios,
    475482\textit{Image halftoning using a visual model in error diffusion}.
     
    479486
    480487\end{document}
    481 
  • research/2008-displacement/paper/serpopt-histo.tex

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    411       \put(-42,1278){\makebox(0,0)[r]{\strut{} 0.3}}%
    412       \csname LTb\endcsname%
    413       \put(-42,982){\makebox(0,0)[r]{\strut{} 0.4}}%
    414       \csname LTb\endcsname%
    415       \put(-42,686){\makebox(0,0)[r]{\strut{} 0.5}}%
    416       \csname LTb\endcsname%
    417       \put(-42,390){\makebox(0,0)[r]{\strut{} 0.6}}%
     388      \color{black}%
     389      \csname LTb\endcsname%
     390      \put(130,435){\makebox(0,0){\strut{}-0.3}}%
     391      \csname LTb\endcsname%
     392      \put(519,435){\makebox(0,0){\strut{}-0.2}}%
     393      \csname LTb\endcsname%
     394      \put(907,435){\makebox(0,0){\strut{}-0.1}}%
     395      \csname LTb\endcsname%
     396      \put(1295,435){\makebox(0,0){\strut{} 0}}%
     397      \csname LTb\endcsname%
     398      \put(1683,435){\makebox(0,0){\strut{} 0.1}}%
     399      \csname LTb\endcsname%
     400      \put(2071,435){\makebox(0,0){\strut{} 0.2}}%
     401      \csname LTb\endcsname%
     402      \put(2460,435){\makebox(0,0){\strut{} 0.3}}%
     403      \put(1295,105){\makebox(0,0){\strut{}$dx$}}%
     404      \csname LTb\endcsname%
     405      \put(-42,2735){\makebox(0,0)[r]{\strut{}-0.1}}%
     406      \csname LTb\endcsname%
     407      \put(-42,2447){\makebox(0,0)[r]{\strut{} 0}}%
     408      \csname LTb\endcsname%
     409      \put(-42,2159){\makebox(0,0)[r]{\strut{} 0.1}}%
     410      \csname LTb\endcsname%
     411      \put(-42,1871){\makebox(0,0)[r]{\strut{} 0.2}}%
     412      \csname LTb\endcsname%
     413      \put(-42,1585){\makebox(0,0)[r]{\strut{} 0.3}}%
     414      \csname LTb\endcsname%
     415      \put(-42,1297){\makebox(0,0)[r]{\strut{} 0.4}}%
     416      \csname LTb\endcsname%
     417      \put(-42,1009){\makebox(0,0)[r]{\strut{} 0.5}}%
     418      \csname LTb\endcsname%
     419      \put(-42,721){\makebox(0,0)[r]{\strut{} 0.6}}%
     420      \put(-636,1728){\rotatebox{90}{\makebox(0,0){\strut{}$dy$}}}%
    418421    }%
    419422    \gplbacktext
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